Question

A radioactive substance decays at $1/32$ of its initial activity in $25$ days. Its half life is

• A. 4 days
• B. 25 days
• C. 5 days
• D. 20 days

Answer 1

Answer: (C)

Here, $t=25$ days,
$R=\left(\frac{1}{32}\right) R_0$
$\tau_{1 / 2}=$ ?
As $R=R_0 e^{-\lambda t}$
or $\left.\frac{R}{R_o}=e^{-\left(\frac{\text{In} 2}{\tau_1} \times t\right.}\right)\left[\because \tau_{1 / 2}=\frac{\text{In2}}{\lambda}\right]$
$32=2^{t / \tau_{1 / 2}} ; 2^5=2^{t / \tau_{1 / 2}}$
$\therefore \tau_{1 / 2}=\frac{t}{5}=\frac{25}{5}=5$ days